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H 1 Mathematical properties of hierarchies of reduced MHD models

Auteurs : Després, Bruno (Auteur de la Conférence)
CIRM (Editeur )

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ITER tokamak reduced MHD models numerical simulation of ELMs weak formulations toroïdal geometry hyperbolic conservation laws energy preservation linear perturbations of MHD equilibrium Rayleigh-Ritz quotients reduced models in 2D Grad-Shafranov equation Navier-Stokes equations

Résumé : Reduced MHD models in Tokamak geometry are convenient simplifications of full MHD and are fundamental for the numerical simulation of MHD stability in Tokamaks. This presentation will address the mathematical well-posedness and the justification of the such models.
The first result is a systematic design of hierachies of well-posed reduced MHD models. Here well-posed means that the system is endowed with a physically sound energy identity and that existence of a weak solution can be proved. Some of these models will be detailed.
The second result is perhaps more important for applications. It provides understanding on the fact the the growth rate of linear instabilities of the initial (non reduced) model is lower bounded by the growth rate of linear instabilities of the reduced model.
This work has been done with Rémy Sart.

Codes MSC :
35L65 - Conservation laws
35Q30 - Stokes and Navier-Stokes equations
65M60 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
76W05 - Magnetohydrodynamics and electrohydrodynamics

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 26/08/14
    Date de captation : 01/08/14
    Collection : Research talks
    Format : QuickTime (.mov) Durée : 01:03:04
    Domaine : PDE ; Numerical Analysis & Scientific Computing ; Mathematical Physics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2014-08-01_Despres.mp4

Informations sur la rencontre

Nom du congrès : CEMRACS : Numerical modeling of plasmas / CEMRACS : Modèles numériques des plasmas
Organisteurs Congrès : Campos Pinto, Martin ; Charles, Frédérique ; Guillard, Hervé ; Nkonga, Boniface
Dates : 21/07/14 - 29/08/14
Année de la rencontre : 2014
URL Congrès : http://smai.emath.fr/cemracs/cemracs14/

Citation Data

DOI : 10.24350/CIRM.V.18557303
Cite this video as: Després, Bruno (2014). Mathematical properties of hierarchies of reduced MHD models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18557303
URI : http://dx.doi.org/10.24350/CIRM.V.18557303

Bibliographie

  1. Després, B., Sart, R. Navier-Stokes hierarchies of reduced MHD models in Tokamak geometry. Hal preprint - http://hal.archives-ouvertes.fr/hal-00796425

  2. Després, B., Sart, R. Reduced resistive MHD in Tokamaks with general density. ESAIM: Mathematical Modelling and Numerical Analysis 46 (2012) no. 5, pp 1081-1106 - http://dx.doi.org/10.1051/m2an/2011078



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